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We study a generalized mean curvature flow involving a positive power of themean curvature and a driving force. In this paper, we first construct all kindsof radially symmetric translating solutions, and then select one of them tosatisfy a prescribed boundary angle in a cylinder. We then consider the flowstarting at an initial hypersurface: showing the a priori estimates (especiallythe uniform-in-time bounds for the mean curvature which guarantee the uniformparabolicity of the corresponding fully nonlinear equation), giving the globalexistence for the solution of the initial boundary value problem, and provingits convergence to the corresponding translating solution. Our study provides acomplete exposition on the influence of the dimension, the power of the meancurvature, the driving force and the boundary angles on the existence andstability of radially symmetric translating solutions.

Translating Solutions of a Generalized Mean Curvature Flow in a Cylinder: I. Constant Boundary Angles